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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 377520e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.e3 | 377520e1 | \([0, -1, 0, -13471, 604870]\) | \(9538484224/26325\) | \(746181493200\) | \([2]\) | \(983040\) | \(1.1511\) | \(\Gamma_0(N)\)-optimal |
| 377520.e2 | 377520e2 | \([0, -1, 0, -18916, 75616]\) | \(1650587344/950625\) | \(431127084960000\) | \([2, 2]\) | \(1966080\) | \(1.4977\) | |
| 377520.e4 | 377520e3 | \([0, -1, 0, 75464, 528640]\) | \(26198797244/15234375\) | \(-27636351600000000\) | \([2]\) | \(3932160\) | \(1.8443\) | |
| 377520.e1 | 377520e4 | \([0, -1, 0, -200416, -34336784]\) | \(490757540836/2142075\) | \(3885892125772800\) | \([2]\) | \(3932160\) | \(1.8443\) |
Rank
sage: E.rank()
The elliptic curves in class 377520e have rank \(0\).
Complex multiplication
The elliptic curves in class 377520e do not have complex multiplication.Modular form 377520.2.a.e
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
